How is the reliability of two systems in parallel calculated?

The reliability of two systems in parallel is calculated using the formula 1 - (1-R1) * (1-R2). This formula is based on the principle that for parallel systems, the overall system will remain functioning as long as at least one of the components is operational.

Here's how this principle works:

1. R1 denotes the reliability of the first system, while R2 represents the reliability of the second system. The term (1-R1) is the failure probability of the first system, and (1-R2) is the failure probability of the second system.

2. By multiplying these probabilities, (1-R1) * (1-R2), you are calculating the likelihood that both systems will fail simultaneously.

3. The expression 1 - (1-R1)*(1-R2) then gives the probability that at least one of the systems is functioning, which corresponds to the reliability of the entire parallel system.

This is a crucial concept in reliability engineering, especially in designing redundant systems for higher reliability, as it allows for increased overall system performance through redundancy.